Cost Functions
Content
Cost Analysis and Estimation
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What Makes Cost Analysis Difficult?
Link Between Accounting and Economic Valuations
Historical Versus Current Costs
Accounting and economic costs often differ.
Replacement Cost
Historical cost is the actual cash outlay. Current cost is the present cost of previously acquired items. Cost of replacing productive capacity using current technology.
Opportunity Cost
Opportunity Cost Concept
Opportunity cost is foregone value. Reflects second-best use.
Explicit and Implicit Costs
Explicit costs are cash expenses. Implicit costs are noncash expenses.
Incremental and Sunk Costs in Decision Analysis
Incremental Cost
Incremental cost is the change in cost tied to a managerial decision. Incremental cost can involve multiple units of output.
Marginal cost involves a single unit of output.
Sunk Cost
Irreversible expenses incurred previously. Sunk costs are irrelevant to present decisions.
Short-run and Long-run Costs
How Is the Operating Period Defined?
At least one input is fixed in the short run. All inputs are variable in the long run.
Fixed and Variable Costs
Fixed cost is a short-run concept. All costs are variable in the long run.
Short-run Cost Curves
Short-run Cost Categories
Total Cost = Fixed Cost + Variable Cost For averages, ATC = AFC + AVC Marginal Cost, MC = ∂TC/∂Q
Short-run Cost Relations
Short-run cost curves show minimum cost in a given production environment.
Short Run Cost Graphs
1.
AFC
Q
MC ATC
3.
AVC
AFC
Q MC intersects lowest point of AVC and lowest point of ATC. When MC < AVC, AVC declines When MC > AVC, AVC rises
2.
AVC
Q
Relationships Among Cost & Production Functions
AP & AVC are inversely related. (ex: one input) AVC = WL /Q = W/ (Q/L) = W/ APL
Q
prod. functions
AP
MPL
As APL rises, AVC falls
cost
AVC MC
L
MP and MC are inversely related MC = dTC/dQ = W dL/dQ = W / (dQ/dL) = W / MPL
cost functions Q
As MPL declines, MC rises
Long-run Cost Curves
Economies of Scale Long-run cost curves show minimum cost in an ideal environment.
Long Run Cost Functions
All inputs are variable (can adjust) in the long run. LAC is long run average cost
SMC2
SAC2 LMC
LMC is flatter than SMC curves.
ENVELOPE of SAC curves
The optimal plant size for a given output Q2 is plant size 2. (A SR concept.) However, the optimal plant size occurs at Q3, which is the lowest cost point overall. (A LR concept.)
LAC
Q2
Q3
Q
Long Run Cost Function (LAC) Envelope of SAC curves
Cost Elasticity and Economies of Scale
Cost elasticity is εC = ∂C/C ÷ ∂Q/Q.
εC < 1 means falling AC, increasing returns. εC = 1 means constant AC constant returns. εC > 1 means rising AC, decreasing returns.
Long-run Average Costs
Economists think that the LAC is Ushaped
Downward section due to:
Product-level economies which include specialization
and learning curve effects. Plant-level economies, such as economies in overhead, required reserves, investment, or interactions among products (economies of scope). Firm-level economies which are economies in distribution and transportation of a geographically dispersed firm, or economies in marketing, sales promotion, or R&D of multi-product firms.
LAC
CRS region
Flat section of the LAC
DRS
MES Max ES Displays constant returns to scale The minimum efficient scale (MES) is the smallest scale at which minimum per unit costs are attained.
Upward rising section of LAC is due to:
Diseconomies of scale. These include transportation costs, imperfections in the labor market, and problems of coordination and control by management. The maximum efficient scale (Max ES) is the largest scale before which unit costs begin to rise. Modern business management offers techniques to avoid diseconomies of scale through profit centers, transfer pricing, and tying incentives to
Economies of Scope
Economies of Scope Concept
Scope economies are cost advantages that stem from producing multiple outputs. Big scope economies explain the popularity of multi-product firms. Without scope economies, firms specialize.
Scope economics often shape competitive strategy for new products.
Exploiting Scope Economies
Cost-volume-profit Analysis
Cost-volume-profit Charts
Cost-volume-profit analysis shows effects of varying scale. Breakeven analysis shows zero profit points of cost coverage.
`
What Makes Cost Analysis Difficult?
Link Between Accounting and Economic Valuations
Historical Versus Current Costs
Accounting and economic costs often differ.
Replacement Cost
Historical cost is the actual cash outlay. Current cost is the present cost of previously acquired items. Cost of replacing productive capacity using current technology.
Opportunity Cost
Opportunity Cost Concept
Opportunity cost is foregone value. Reflects second-best use.
Explicit and Implicit Costs
Explicit costs are cash expenses. Implicit costs are noncash expenses.
Incremental and Sunk Costs in Decision Analysis
Incremental Cost
Incremental cost is the change in cost tied to a managerial decision. Incremental cost can involve multiple units of output.
Marginal cost involves a single unit of output.
Sunk Cost
Irreversible expenses incurred previously. Sunk costs are irrelevant to present decisions.
Short-run and Long-run Costs
How Is the Operating Period Defined?
At least one input is fixed in the short run. All inputs are variable in the long run.
Fixed and Variable Costs
Fixed cost is a short-run concept. All costs are variable in the long run.
Short-run Cost Curves
Short-run Cost Categories
Total Cost = Fixed Cost + Variable Cost For averages, ATC = AFC + AVC Marginal Cost, MC = ∂TC/∂Q
Short-run Cost Relations
Short-run cost curves show minimum cost in a given production environment.
Short Run Cost Graphs
1.
AFC
Q
MC ATC
3.
AVC
AFC
Q MC intersects lowest point of AVC and lowest point of ATC. When MC < AVC, AVC declines When MC > AVC, AVC rises
2.
AVC
Q
Relationships Among Cost & Production Functions
AP & AVC are inversely related. (ex: one input) AVC = WL /Q = W/ (Q/L) = W/ APL
Q
prod. functions
AP
MPL
As APL rises, AVC falls
cost
AVC MC
L
MP and MC are inversely related MC = dTC/dQ = W dL/dQ = W / (dQ/dL) = W / MPL
cost functions Q
As MPL declines, MC rises
Long-run Cost Curves
Economies of Scale Long-run cost curves show minimum cost in an ideal environment.
Long Run Cost Functions
All inputs are variable (can adjust) in the long run. LAC is long run average cost
SMC2
SAC2 LMC
LMC is flatter than SMC curves.
ENVELOPE of SAC curves
The optimal plant size for a given output Q2 is plant size 2. (A SR concept.) However, the optimal plant size occurs at Q3, which is the lowest cost point overall. (A LR concept.)
LAC
Q2
Q3
Q
Long Run Cost Function (LAC) Envelope of SAC curves
Cost Elasticity and Economies of Scale
Cost elasticity is εC = ∂C/C ÷ ∂Q/Q.
εC < 1 means falling AC, increasing returns. εC = 1 means constant AC constant returns. εC > 1 means rising AC, decreasing returns.
Long-run Average Costs
Economists think that the LAC is Ushaped
Downward section due to:
Product-level economies which include specialization
and learning curve effects. Plant-level economies, such as economies in overhead, required reserves, investment, or interactions among products (economies of scope). Firm-level economies which are economies in distribution and transportation of a geographically dispersed firm, or economies in marketing, sales promotion, or R&D of multi-product firms.
LAC
CRS region
Flat section of the LAC
DRS
MES Max ES Displays constant returns to scale The minimum efficient scale (MES) is the smallest scale at which minimum per unit costs are attained.
Upward rising section of LAC is due to:
Diseconomies of scale. These include transportation costs, imperfections in the labor market, and problems of coordination and control by management. The maximum efficient scale (Max ES) is the largest scale before which unit costs begin to rise. Modern business management offers techniques to avoid diseconomies of scale through profit centers, transfer pricing, and tying incentives to
Economies of Scope
Economies of Scope Concept
Scope economies are cost advantages that stem from producing multiple outputs. Big scope economies explain the popularity of multi-product firms. Without scope economies, firms specialize.
Scope economics often shape competitive strategy for new products.
Exploiting Scope Economies
Cost-volume-profit Analysis
Cost-volume-profit Charts
Cost-volume-profit analysis shows effects of varying scale. Breakeven analysis shows zero profit points of cost coverage.
